bhartiyam 12... · 3. what is triple fusion where and how it takes place. name the nuclei developed...

BHARTIYAM INTERNATIONAL SCHOOL Discover beyond ordinary…

Rudrapur, Distt. Udham Singh Nagar, Uttarakhand ( India)

PHYSICS



CHAPTERWISE IMPORTANT QUESTIONS NAME:-____________________ CLASS: - XII

REPRODICTION IN ORGANISMS

1. Offspring derived by asexual reproduction are called as clones. Justify giving two reasons.

2. Why in the external type of fertilization large amount of gametes are released in the medium.

3. Why is reproduction essential for organisms?

4. Offspring formed due to sexual reproduction have better chances of Survival. Why? Is the statement always

true?

5. Why are the offspring of oviparous animals at a greater risk as compared to offspring of viviparous animals?

6. What is zygote? Do you agree zygote is vital link that ensures continuity of species?

SEXUAL REPRODUCTION IN FLOWERING PLANTS

1. What is meant by monosporic development of female gametophyte?

2. What is meant by emasculation? When and why do the plant breeders employ this technique?

3. What is triple fusion where and how it takes place. Name the nuclei developed in triple fusion.

4. Explain the process of pollination in vallisneria. How is it different in water lily which is also an aquatic plant?

5. i) Can a plant flowering in Mumbai is pollinated by pollen grain of the same species growing in New Delhi

provide explanation to your answer.

ii) Draw the diagram of a pistil where pollination has successfully occurred label the parts involved in reaching

the male gamete to its desire destination

6. i) How are parthenocarpic fruits produced by some plants and appomattox seeds by some others. Explain?

ii) How does a farmer use the dormancy of seeds to his advantage?

HUMAN REPRODUCTION

1. What is scrotum? write a note on it.

2. Name the hormones involved in regulation of spermatogenesis.

3. How and at what stage of the menstrual cycle is Corpus luteum formed in human female where does it

regress?

4. During the reproductive cycle of human female when where and how does a placenta develop? What is the

function of placenta during the pregnancy and embryo development?

5. Write the functions of following

Corpus luteum

Endometrium

Acrosome

Sperm tail

Fimbriae

Leydig cells

Primary spermatocyte

5. Medically it is advised to all young mothers that breastfeeding is the best for their newborn babies Do you

agree? Give reasons in support of your answer.

6. Explain the zygote intrafallopian transfer (ZIFT). How is intra Uterine technique (IUT) different from it?



PRINCIPLES OF INHERITANCE AND VARIATION

1. Mention the advantages of selecting the pea plant for experiment by Mendel.

2. Write the conclusion mendel arrived at on dominance of traits on the basis of monohybrid cross that he carried

out in pea plant .Explain why a recessive allele is unable to express itself in heterozygous state?

3. Define and design a test cross.

4. Give an example of an autosomal recessive trait in human. Explain its pattern of inheritance with the help of

cross.

5. Explain sex determination mechanism in humans. How is it different in birds?

6. i) what do Y and B stand for in why YAC and BAC used in human genome Project (HGP)? Mention their role in

the project.

ii) Write the percentage of total human genome that codes for proteins and the percentage of discovered genes

whose functions are known as observed during HGP.

iii) expand SNPs identified by scientist in HGP.

MOLECULAR BASIS OF INHERITANCE

1. State the dual role of deoxyribonucleoside triphosphate during the DNA replication.

2. How do histones acquire positive charge?

3. In the medium where E.coli was growing lactose was added, which induce the lac operon.Then why does lac

operon shut down some time after addition of lactose in the medium?

4. What is DNA fingerprinting? Mention its application.

5. What is euchromatin and heterochromatin?

6. List two essential roles of ribosomes during translation.

7. Unambiguous, universal and degenerates are some of the terms used for genetic code explain salient feature

of each of them.

8. Give the schematic representation of lac operon of E.coli. Explain the functioning of disappear on when lactose

is provided in the growth medium of the bacteria.

9. list the structural genes involved in the digestion of lactose in E coli. Highlight the function of any one. What

triggers the transcription of these genes?

10. What is aminoacylation? State its significance. Discuss the role of enzyme DNA ligase plays during DNA

replication.

EVOLUTION

1. What is convergent evolution? Provide some examples for analogy.

2. What is founder effect according to Hardy- Weinberg's principle?

3. State the theory of biogenesis how does miller's experiment support this theory?

4. Divergent evolution lead to homologous structures explain with the help of an example.

5. Explain adaptive radiation with the help of suitable example.

HUMAN HEALTH AND DISEASE

1. Name two human disease caused due to protozoa and provide their causal organism and their symptoms.

2. Name any two organism that are responsible for causing ringworm in humans. Mention two diagnostic

symptoms. Name the specific part of human body where these organisms thrive and explain why?

3. How is an allergic reaction caused by an allergen? Name a drug that can reduce the symptom of allergy.

4. What is meant by metastasis?

5. List harmful effect caused by alcohol and drugs?

6. What is the mechanism by which the AIDS virus causes deficiency of immune system of the infected person?



7. Write a note on Coca, an alkaloid?

8. What are the various public health measures, which you would suggest as safeguard against infectious

disease?

9. What is innate immunity? What are the barriers in it? What is cytokinin barrier?

10. How are cancerous cells different from normal cells?

STRATEGIES FOR ENHANCEMENT IN FOOD RESOURCE

1. Explain inbreeding depression and how can it be overcome?

2. What is cross breeding? What is significance of cross breeding in animal breeding Programme?

3. If your family owned a dairy farm what measures would you undertake to improve the quality and quantity of

milk production?

4. What is plant breeding? Give various steps that are followed during plant breeding.

5. Explain what is meant by biofortification.

6. What is totipotency? What is the tissue culture technique?

7. Explain out-breeding, out-crossing and cross-breeding practices in animal husbandry.

8. Plant breeding technique has helped sugar industry in North India. Explain how.

9. List the two steps that are essential for carrying out artificial hybridization in crop plants and why?

10. Your advice is sought to improve the nitrogen content of the soil to be used for cultivation for a non

leguminous terrestrial crop.

i) Recommend to microbes that can enrich the soil with nitrogen

ii) Why do leguminous crops not require such enrichment of the soil?

MICROBES OF HUMAN WELFARE

1. Name the enzyme produced by streptococcus bacteria. Explain its importance in medical science. 2. What is biological oxygen demand? How it suggest the quality of water body? 3. What is biofertilizer? Give its significance 4. Explain the significant role of the genus nucleopolyhedrovirus in an ecological sensitive area. 5. Find out the role of microbes in the following- i) Single cell protein ii) Soil.

BIOTECHNOLOGY PRINCIPLES AND PROCESS 1. What are the important steps of recombinant DNA technology?

2. Name and describe the technique that helps in separating the DNA fragment formed by the use of restriction

endonuclease.

3. Explain palindromic nucleotide sequence with the help of suitable example.

4. What are the basic features required to achieve cloning into a vector?

5. What is a GMO. list five possible advantages of a GMO to a farmer.

6. Suggest and describe a technique to obtain multiple copies of a gene of interest in vitro.

7. Explain enzyme replacement therapy to treat adenosine deaminase deficiency. Mention two disadvantages of

this procedure.

8. Why do lepidopteran die when they feed on BT cotton plant explain how does it happen.

9. Describe the roles of heat primers and the bacterium thermus aquaticus in the process of PCR.

10. Name and describe the technique that helps in separating the DNA fragment formed by the use of restriction

endonuclease.



BIOTECHNOLOGY AND ITS APPLICATION

1. What is gene therapy? Illustrate using example of adenosine deaminase (ADA) deficiency.

2. Explain the role of Ti plasmid in biotechnology.

3. How is Bt cotton made to attain resistance against the ball worm?

4. Explain the process of RNA interference.

5. Explain the steps involved in the production of artificial insulin.

6. What is biopiracy? State the initiative taken by the Indian parliament towards it.

7. i) Why must a cell made competent in biotechnology experiments? How a calcium ion does helps in doing so?

ii) State the role of wireless stick gun in biotechnology experiments.

8. i) how has the development of bioreactor helped in biotechnology?

ii) Name the most commonly used bioreactor and describe its working.

9. How Rosie is considered different from a normal cow? Explain.

10. What is insecticidal protein?

ORGANISM AND POPULATION

1. What is allen's rule? Provide example to justify it.

2. How is diapause different from hibernation?

3. Name the important defence mechanism in the plant against herbivory.

4. State various type of parasitism shown by organisms

5. Explain the birth rate and death rate in population with the help of an example what is age pyramid?

6. How does monarch butterfly defend itself from the Predator? Explain.

7. Explain brood parasitism with the help of an example.

8. Why do clownfish and sea anemone pair up. What is the relationship called?

9. Pollinating species of wasp shows mutualism with specific fig plant. Mention the benefits the female wasps

derived from the fig tree from such an interaction.

10. Plants that inhibit a rainforest are not found in a wetland. Explain.

ECOSYSTEM

1. What are the various aspects that are considered while studying an ecosystem? 2. What is primary productivity why does it vary in different type of ecosystem state the relationship between gross and net primary productivity. 3. What is the importance of fragmentation and leaching processes? 4. What are the characteristic features of Climax community? 5. In most of ecosystem all the three pyramids are applied what does this means? 6. What is hydrarch succession? Name the Pioneer species in this type of succession. 7. Name the two types of nutrient cycles existing in nature. Where are their reservoirs present. State the function of reservoirs. 8. Plenty of algal bloom is observed in a pond in your locality i) Write what has caused this bloom and how does it affect the quality of water. ii) Suggest a preventive measure. 9. Why is the rate of secondary succession faster than that of primary succession? 10. There is a unidirectional flow of energy from sun to the consumers. Why?



BIODIVERSITY AND CONSERVATION

1. Why certain region have been declared as biodiversity hotspots by environmental list of the world. Name any

two hotspots in India.

2. Why genetic diversity is important?

3. Explain with the help of suitable example that three different ways by which organisms overcome their stressful

condition lasting for short duration.

4. Name and describe any three causes of biodiversity losses.

5. Biodiversity must be conserved as it plays an important role in many ecosystem services that nature provides.

Explain any two services of ecosystem.

6. What are sacred groves? What is their role in conservation?

7. Explain the hypothesis postulated by Stanford equal or just Paul Ehrlich.

8. What is the significance of slope of regression in species area relationship?

9. Suggest to practice is giving one example of each that help protect him and threatened species.

10. Mention the kinds of biodiversity of more than a hundred varieties of mangoes in India represent how it is

possible?

ENVIRONMENTAL ISSUES

1. What are the harmful effect on human health which are caused due to particulate matter?

2. How does an electrostatic precipitator work to remove the particulate pollutant released from the thermal power

plant?

3. What steps were taken by government of Delhi to control air pollution?

4. How is biomagnification of DDT notorious for birds species?

5. State the cause of accelerated eutrophication.

6. What are the anthropogenic activities that can convert a fertile land into an array non cultivable one?

7. Explain the relationship between cfcs and ozone in the stratosphere.

8. list the events that reduce the biological oxygen demand board of primary effluent during sewage treatment

9. list the events that lead to biogas production from wastewater whose body has been reduced significantly.

10. State the function of catalytic converter in an automobile.

Bhartiyam International School QUESTION BANK (2018-19)

Subject: Accountancy

Class: XII (C)

ACCOUNTING FOR PARTNERSHIP FIRMS- FUNDAMENTALS

1. P and Q were partners in a firm sharing profits and losses equally. Their fixed capitals were

Rs.2,00,000 and Rs. 3,00,000 respectively. The partnership deed provided for interest on

capital @12% per annum. For the year ended 31st March, 2016, the profits of the firm were

distributed without providing interest on capital. Pass necessary adjustment entry to rectify

the error.

2. AXIS Bank Ltd. earned a profit of ₹ 3,25,000 during the year ending on 31st Mach, 2016.

They have decided to donate 10% of this profit to an NGO working for senior citizens. Pass

necessary journal entries for the distribution of profits.

3. A, B and C were partners in a firm. Their fixed capitals were Rs 3,00,000, Rs 2,00,000 and

Rs 2,00,000 respectively. According to the partnership deed they were entitled to interest on

capital @ 5% p.a. in addition B was also entitled to draw a salary of Rs 5,000 per month. C

was entitled to a commission of 10% on the profits after charging interest on capital but

before charging salary payable to B. The net profit for the year was Rs 2,10,000 distributed in

the ratio of their capitals without providing for any of the above adjustments. The remaining

profits were to be shared in the ratio of 2:2:1. Pass the necessary adjustment entry showing

the working clearly.

4. X and Y are partners in a firm. They agree on the following:

X is entitled to a salary of Rs 500 per month together with a commission of 10% of the net

profit after charging salary, but before charging any commission. Y is entitled to a salary of

Rs 3,000 p.a. together with a commission of 8% of Net Profit after charging Salary and all

commissions. Net Profit before charging any commission but after charging salary is Rs

60,000.

Prepare Profit and Loss Appropriation Account.

CHANGE IN PROFIT SHARING RATIO

5. The combined capital of Arun and Varun is Rs 2,00,000 and the market rate of interest is

12%. Annual salary to partners is Rs 5,000 each. The profits for the last three years were Rs

32,000, Rs 45,000 and Rs 55,000. Goodwill is to be valued at 2 years purchase of the last

three year‟s average super profits. Calculate the goodwill of the firm.

6. Rahul and Rohit are partners sharing profits in the ratio of 1:2. They admit Sohan for ¼th

share, which he acquires from Rahul. Find the new profit sharing ratio.

7. Give the journal entry to distribute „Workmen Compensation Reserve‟ of Rs 70,000 at the

time of retirement of Neeti when there is a claim of Rs 25,000 against it. The firm has three

partners Raveena, Neeti and Rajat.

8. P and Q are partners sharing profits in the ratio of 5:3. R is admitted and the new ratio is

4:3:2. What will be the sacrificing ratio?

ADMISSION OF A PARTNER

9. A and B are partners sharing profits. They admit C as a new partner. C contributes Stock Rs

30,000; Furniture Rs 40,000; Machinery Rs 1,00,000 and Cash Rs 20,000 towards his capital

and Goodwill. Goodwill on the date of admission was valued at Rs 1,80,000. Calculate C‟s

share of Goodwill and Capital.

10. A and B are partners sharing profits and losses as 2:1. C and D are admitted and profits

sharing ratio becomes 4:2:3:1. Goodwill is valued at Rs. 2,00,000. D brings required goodwill

and Rs. 50,000 cash for capital. C brings in Rs. 50,000 cash and Rs. 40,000 worth stock as his

capital in addition to the required amount of goodwill in cash.

11. Gaurav and Saurabh are partners in a firm having capital balance of Rs 90,000 and Rs 60,000

respectively. They admitted Mohan as a new partner for 2/7th share in the firm. What will be

Mohan‟s share of capital if he has to contribute capital in proportion to his profit sharing

ratio?

12. Karan and Amit were partners sharing profits and losses in the ratio of 3:2. On 1st April, 2015,

Kritika was admitted for 1/5th share. Balance Sheet of Karan and Amit on 31

st March, 2015

was as under:

Liabilities Rs Assets Rs

Capitals:

Karan

Amit

Employees Provident Fund

Workmen Compensation Fund

Sundry Creditors

40,000

20,000

10,000

16,000

7,500

93,500

Plant and Machinery

Furniture

Profit & Loss A/c

Sundry Debtors

Cash in Hand

18,000

40,000

25,000

9,000

1,500

93,500

Additional Information: On the above date Kritika was admitted with the following terms:

(a) Kritika will bring Rs 20,000 for her capital and Rs 5,000 for her share of goodwill

premium.

(b) Provision for doubtful debts is to be created @ 5%.

(c) There was a liability of Rs 6,000 for workmen compensation.

(d) There was a unrecorded furniture for Rs 5,000.

(e) Capitals of Karan and Amit to be adjusted on the basis of Kritika‟s capital through cash.

Prepare Revaluation A/c, Partner‟s Capital A/c s and Balance Sheet.

RETIREMENT OR DEATH OF A PARTNER

13. Ravi, Mukesh, Naresh and Yogesh are partners in a firm sharing profits and losses in the

Ratio of 2:2:1;1. Mukesh and Naresh decided to retire from the firm. The goodwill of the firm

was valued at Rs.90,000. Ravi and Yogesh decided to share future profits and losses in the

ratio of 3:2. Pass necessary journal entry.

14. X, Y and Z are partners in a firm. Total capital employed is Rs 5,40,000 contributed by them

in their profit sharing ratio. Y retires from the firm. On the day of retirement the firm had a

balance of Rs 90,000 in the General Reserve Account. Y took one of the unrecorded assets of

the firm valued at Rs 54,000 in part payment and, balance amount was paid in cash. Pass

necessary entries on Y‟s retirement.

15. A, B and C are sharing profits in the ratio of 3 : 2 : 1. C dies on 30th June, 2011. Accounts are

closed on 31st March every year. Sales for the year ending 31

st March, 2011 amounted to Rs

90,00,000. Sales from 1st April 2011 to 30

th June 2011 amounted to Rs 36,00,000. The profit

for the year ending 31st March, 2011 amounted to Rs 4,50,000. Calculate the deceased

partner‟s share in the current year‟s profits.

16. The Balance Sheet of A,B and C who were sharing profits in the ratio of 1:2:2 as on 31

March, 2015 was as follows:

Balance Sheet as at 31st March, 2015


General Reserve

Bills Payable

Loan

Capital A/c:

A 48,000

B 36,000

C 60,000

6,000

12,000

13,200

1,44,000

1,75,200

Cash

Stock

Investments

Land and Building

A‟s Loan

15,600

38,400

51,000

58,200

12,000

1,75,200

A died on 31st July, 2015. The Partnership Deed provided for the following on the death of a

partner:

(i) Goodwill of the firm is valued at two year‟s purchase of the average profit for the last

three years.

(ii) A share of profit or loss till the date of his death was to be calculated on the basis of sales.

Sales for the year ended 31st March, 2015 amounted to Rs 3,00,000 and from 1

st April,

2015 to 31st July, 2015 amounted to Rs 1,83,000. The profit for the year ended. 31

st

March, 2015 was Rs 75,000.

(iii) Interest on capital was to be provided @ 8% p.a.

(iv) The average profit for the last three years was Rs 33,000.

Prepare A‟s Capital Account to be rendered to his Executor.

17. Amit, Sumit and Nimit are partners in a firm sharing profits in ratio 5:4:1. Their Balance

Sheet as at 31st March, 2015 was as follows:


Capital Accounts:

Amit 85,000

Sumit 54,000

Nimit 36,000

General Reserve

Outstanding Expenses

Creditors

1,75,000

20,000

14,000

47,000

2,56,000

Goodwill

Land

Machinery

Patents

Stock

Debtors

Bank

27,000

64,000

34,000

2,000

25,000

50,000

54,000

2,56,000

It was agreed that Amit will retire on the following terms:

(i) The Goodwill of the firm is valued at two years purchase of the average annual profits of

the preceding three years. The profits for the last three years were Rs 34,000, Rs 42,000

and Rs 50,000.

(ii) Provision for doubtful debts at 10% on Debtors to be created.

(iii) Land revalued at Rs 82,000 and Machinery at Rs 24,000.

(iv) Sundry Creditors have agreed to accept 5% less.

(v) Patents were valueless. Prepare Revaluation A/c, Partner‟s Capital Accounts and the

Balance Sheet of the newly constituted firm.

DISSOLUTION OF A PARTNERSHIP FIRM

18. On dissolution, what entry is passed if a partner takes over an asset of the firm valued Rs

10,000 at Rs 6,000?

19. A, B and C were partners in a firm sharing profits in a ratio of 2 : 2 : 1. On 28th February,

2017, their firm was dissolved. From the following information complete realisation account,

partners‟ capital account and cash account.

Realisation Account

Particulars Amt (₹) Particulars Amt (₹)

To Sundry Assets A/c

To A‟s Capital A/c (Creditors)

To B‟s Capital A/c (Realisation

expenses)

2,60,000

1,50,000

10,000

4,20,000

By Creditors

By C‟s Capital A/c (Sundry assets)

By ...................

1,60,000

1,30,000

.........

4,20,000

Partners’ Capital Account

Particulars A (₹) B (₹) C (₹) Particulars A (₹) B (₹) C (₹)

To Balance b/d

To ..............

-

........

-

........

46,000

........

By Balance b/d

By Realisation A/c

1,50,000

........

10,000

........

-

-

To Realisation

A/c (Assets)

To Cash A/c

(Final payment)

-

2,48,000

3,00,000

-

-

52,000

1,30,000

-

2,02,000

By Cash A/c

(Cash brought in)

-

3,00,000

32,000

52,000

2,02,000

2,02,000

Cash Account

Particulars Amt (₹) Particulars Amt (₹)

To Balance b/d

To ...............

To ...............

14,000

........

........

2,48,000

By .............. .........

2,48,000

20. Pass the necessary journal entries for the following transactions on the dissolution of the firm

of Sudha and Shiva after the various assets (other than cash) and outside liabilities have been

transferred to Realisation Account:

(i) Sudha agreed to pay off her husband‟s loan Rs 19,000.

(ii) A debtor whose debt of Rs 9,000 was written off in the books paid Rs 7,500 in full

settlement.

(iii) Shiva took over all investments at Rs 13,300.

(iv) Sundry creditors Rs 10,000 were paid at 9% discount.

(v) Realisation expenses Rs 3,400 were paid by Sudha for which she was allowed Rs

3,000.

(vi) Loss on realisation Rs 9,400 was divided between Sudha and Shiva in 3:2 ratio.

COMPANY ACCOUNTS- ISSUE OF SHARES

21. X Ltd. forfeited 150 shares of Rs 20 each issued at a premium of Rs 5 per share for the non

payment of the seconds and final call of Rs 7 per share. 100 of these shares were reissued @

Rs 21 per share fully paid. Journalise the above transactions regarding the forfeiture and

reissue.

22. Ram Ltd invited applications for 8,00,000 equity shares of ₹ 10 each at a premium of ₹ 40

per share. The amount was payable as follows

On application - ₹ 35 per share (including ₹ 30 premium)

On allotment - ₹ 8 per share (including ₹ 4 premium)

On first and final call – Balance

Applications for 7,70,00 shares were received. Shares were allotted to all the applicants.

Sumit to whom 70,000 shares were allotted failed to pay the allotment amount. His shares

were forfeited immediately after allotment.

Afterwards the first and final call was made. Sohail, the holder of 5,000 shares failed to pay

the first and final call. His shares were also forfeited. Out of the forfeited shares 10,000 shares

were reissued at ₹ 50 per share fully paid-up. The reissued shares included all the shares of

Sohail.

23. Pass necessary journal entries for the above transactions in the books of Ram Ltd.

24. Z X Limited issued applications for issuing Rs.5,00,000 equity shares of Rs 10 each payable

at a premium of Rs 10 each payable with Final call. Amount per share payable as follows:

on application Rs 2

on allotment Rs 3

on first call Rs 2

on second and final call balance

Applications for Rs 8,00,000 shares were received. Applications for 50,000 shares

were rejected and application money was refunded. Allotment was made to the remaining

applicants as follows:

Category number of shares applied number of shares allotted

I 2,00,000 1,50,000

II 5,50,000 3,50,000

Excess application money received with applications was adjusted towards sum due on

allotment. Balance if any was adjusted towards future calls. Govind , a shareholder belonging

to category I,to whom 1500 shares were allotted, paid his entire share money with allotment.

Manohar belonging to category II, who had applied for 11,000 shares failed to pay second and

final call money. Manohar‟s shares were forfeited after the final call. The forfeited shares

were reissued at 10 per share as fully paid up. Assuming that the company maintains call in

advance account and call in arrears account. Pass necessary journal entries for the above

transaction in the books of Z X Limited.

COMPANY ACCOUNTS - ISSUE & REDEMPTION OF DEBENTURES

25. Pass necessary journal entries for the following

a) Issued 1,000, 7% debentures of Rs 100 each at 5% discount and redeemable at par.

b) Mahima Ltd. issued 1,500, 12% debentures of Rs 100 each at a discount of 10%,

redeemable at a premium of 5%.

26. On 1st April 2013 XY Limited issued 9,00,000, 10% debentures at a discount of 9%. The

debentures were to be redeemed in 3 equal annual installments starting from 31st March

2015. Prepare discount on issue of debenture account for the first three years starting from 1st

April 2013. Also show your working carefully.

27. X Ltd. has Rs.10,00,000, 9% debentures due to be redeemed out of profits on 1st October,

2009 at a premium of 5%. The company had a debenture redemption reserve of Rs.4,14,000.

Pass necessary journal entries at the time of redemption.

28. Arihant Ltd on 1st April, 2014 acquired assets of the value of ₹ 12,00,000 and liabilities

worth ₹ 1,40,000 from Sultan Ltd at an agreed value of ₹ 11,00,000. Arihant Ltd issued 12%

debentures of ₹ 100 each at a premium of 10% in full satisfactions of purchase consideration.

The debentures were redeemable 3 years later at a premium of 5%. Pass entries to record the

above, including redemption of debentures.

FINANCIAL STATEMENTS OF A COMPANY

29. State any two objectives of financial statement analysis.

30. Name any two items that are shown under the head “Other Current Liabilities” and any two

items that are shown under the head “Other Current assets” in the balance sheet of a company

as per schedule III of the companies Act, 2013.

31. Under which major heading and sub-heading will the following itemsbe shown in the balance

sheet of a company as per Schedule III Part I of the companies Act,2013.

(i) Net loss shown by statement of Profit and Loss

(ii) Capital Redemption Reserve

(iii) Bonds

(iv) Loans repayable on demand

(v) Unpaid dividend

(vi) Buildings

FINANCIAL STATEMENT ANALYSIS

32. State any two objectives of financial statement analysis.

33. State any two limitations of financial statement analysis.

34. Name any two tools of analysis of financial statement.

35. From the following statement of profit and loss of Suntrack Ltd. for the year ended 31st

March,2014 and 2015, prepare a „Comparative Statement of Profit and Loss‟:

(4)

Particulars Note 2014-2015(Rs.) 2013-2014(Rs.)

Revenue from operation

Other income

Expenses

20,00,000

12,00,000

13,00,000

12,00,000

9,00,000

10,00,000

36. From the information given below, prepare Comparative Statement of Profit & Loss:

Particulars 31st March 2013 31

st March 2012

A. Revenue from operations: Sales

B. Sales Return

C. Cost of Material consumed

D. Other expenses

%(Net revenue from operations-

cost of material consumed)

E. Income tax

Rs 24,00,000

Rs 4,00,000

50% of Revenue from

operations( Net)

10%

40%

Rs 21,00,000

Rs 1,00,000

60% of Revenue from

operations( Net)

20%

40%

ACCOUNTING RATIO

37. The quick ratio of a company is 0.8:1. State with reason whether the following transactions

will increase, decrease or not change the quick ratio.

a. Purchase of loose tools Rs. 2,000

b. Insurance premium paid in advance Rs.500

c. Sale of goods on credit Rs.3,000

d. Honoured a bills payable Rs.5,000 on maturity.

38. From the following information, calculate inventory turnover ratio.

Revenue from operations Rs. 4,00,000, average inventory Rs.55,000. The rate of gross loss on

revenue from operations was 10%.

39. X Ltd. has a current ratio of 3.5:1 and quick ratio of 2:1. If excess of current assets over

quick assets represented by inventory is Rs.24,000, calculate current assets and current

liabilities.

40. From the following information calculate „Interest coverage ratio‟.

Profit after interest and tax Rs.4,97,000

Rate of income tax 30%

12% debentures Rs.6,00,000

CASH FLOW STATEMENT

41. Short-term investments are not considered while preparing cash flow statement. Why?

42. State the primary objective of preparing a cash flow statement.

43. „Cheques and drafts in hand‟ are not considered while preparing cash flow statement. Why?

44. Following is the Balance Sheet of Karan & Sons Ltd. as at 31st March, 2015

Karan & Sons Ltd

BALANCE SHEET as at 31st March, 2015 and 2014

Particulars Note

No.

31-3-2015 31-3-2014

I. EQUITY & LIABILITIES:

(1) Shareholder’s Fund:

a) Share Capital

b) Reserves &Surplus

(2) Current Liabilities:

a) Trade Payables

b) Short-term Provisions

1

2

3

2,50,000

2,60,000

49,500

50,000

2,25,000

1,15,000

37,500

40,000

TOTAL 6,09,500 4,17,500

II. ASSETS:

(1)Non-Current Assets:

Fixed Assets:

(1) Tangible Assets

(2) Intangible Assets

(2)Current Assets:

a) Inventory

b)Trade Receivables

4

5

2,80,000

20,000

15,000

2,84,000

2,40,000

36,000

10,000

1,19,000

c) Cash & Cash Equivalents 10,000 12,500

TOTAL 6,09,000 4,17,500

Notes to Account

Particulars

31-3-2015 31-3-2014

(1) Share Capital:

Equity share capital

Preference share capital

(2) Reserve and Surplus:

General Reserve

Profit & Loss account

(3) Short term provisions:

Provision for tax

(4) Tangible Assets:

Building

Plant

(5) Intangible Assets:

Goodwill

2,00,000

50,000

2,50,000

1,25,000

1,35,000

2,60,000

50,000

1,80,000

1,00,000

2,80,000

20,000

1,50,000

75,000

2,25,000

70,000

45,000

1,15,000

40,000

2,00,000

40,000

2,40,000

36,000

Additional information:

(1) Depreciation charged on Plant was ₹10, 000 and on Building ₹ 60,000.

(2) Income Tax paid during the year amounted ₹43, 000

Prepare Cash Flow Statement.



Name: _____________ Subject: Economics Class: XII C

Part 1 : MICRO-ECONOMICS Unit I: Introduction

Chapter 1 : Introduction to Economics

(1 Marks Ques)

1. Define Positive & Normative economics.

2. Why does an economic problem arise.

3. Give 2 example of micro-economic study.

4. Define MOC & MRT?

5. Why PPC is concave to the point of origin?

(2 Marks Ques)

6. Distinguish between Micro and Macro Economics.

7. Production in an economy is below to its potentially due to unemployment. Government starts employment

generation schemes. Explain it effects by using PPC.

8. Explain the effects of unfavourable conditions in Jammu & Kashmir on its PPF.

9. Explain central problem of “What to produce” or “How to produce” or “for whom to produce”.

10. Define MOC & MRT with the help of a hypothetical numerical example.

(6 Marks Ques)

11. Why do central problem arise in an economy? Explain central problems of an Economy?

12. Assuming that no resource is equally efficient in production of all goods, name the curve which shows

production potential of the economy. Explain, giving season, its properties.

UNIT : II Consumer’s Equilibrium & Demand

Chapter : 2 Consumer Equilibrium

(1 Marks Ques)

1. Define Total Utility & Marginal Utility.

2. Why is the study of consumer‟s equilibrium subject matter of micro-economics?

3. Explain why is Budget line negatively sloped?

4. What do you mean by Monotonic preferences.

5. Giving reasons, state whether the following statement is

TRUE or FALSE

(i) MU can never be negative

(ii) A budget set is a collection of such bundles of goods that give same satisfaction.

(3 – 4 Marks Ques)

6. Differentiate bet cardinal & orelinal utility analysis

7. Explain law of diminishing marginal utility.

8. Explain consumer‟s equilibrium in case of a single commodity with the help of a utility schedule.

9. A consumer consumes 2 goods A & B and is in equilibrium. Show that why price of good B falls demand

for B rise. Answer this question with the help of utility analysis.

10. Define Budget line. Explain why it is a straight line.



(6 Marks Ques)

11. Explain the concepts of Marginal Rate of Substitution. Explain the reaction of the consumer when MRS is

higher than the ratio of prices.

12. Explain the conditions of Consumer‟s Equilibrium under indifference curve analysis.

Chapter 3 : Theory of Demand

(1 Mark Ques)

1. Ceteris Paribus, if the government provides subsidice on electricity bills, what would be the likely change in

the market demand of desert cooler.

2. What causes an upward movement along a demand curve of a commodity?

3. What is meant by inferior goods and normal goods in economics?

4. The demand for a commodity always increases with increase in the price of other goods. TRUE or FALSE

5. Give on reason for a leftwards shift in demand curve.


6. Explain the effect of (a) change in own price & (b) change in price of substitute

7. How does change in price of complementary good affects the demand of the given good? Explain with the

help of an example.

8. Distinguish between demand of an individual & market demand with the help of a schedule.

9. Explain the relation between Goods x & Good Y in each case, if with a fall in price of X demand for goods

Y (i) rises and (ii) falls? Give reasons.

10. Explain law of demand with the help of a demand schedule.

(6 Marks Ques)

11. Explain relationship between:

12. Explain with the help of diagrams the effect of the following changes on the demand of a commodity (i) a

fall in price of substitute good (ii) A rise in price of complementary goods.

Chapter 4 : Elasticity of Demand

(1 Marks Ques)

1. When is the Demand for a good said to be perfectly inelastic.

2. Arrange the following coefficients of price elasticity of demand in ascending order :

– 0.7, – 0.3, – 1. 1, – 0. 8

3. Why demand for water is inelastic?


4. What will be the effect of 10 percent rise in price of a good on its demand if price elasticity of demand is

(a) zero (b) –1 (c) –2

5. A consumer buys 10 units of a commodity at a price of Rs 10/ unit. He incurs an expenditure of Rs 200 on

buying 20 units. Calculate price elasticity of demand by the percentage method. Comment upon the shape

of demand curve based on this information.



6. Calculate price elasticity of demand by percentage method:

7. A consumer buys 18 units of a good at a price of Rs 9/ unit. The price elasticity of demand for the good is

(–) 1. How many units the consumer will buy at a price of Rs 10 per unit? Calculate.

8. The price Elasticity of Demand for a good is –(0.4), if its price increases by 5% by what percentage will its

demand fall. Calculate.

(6 Marks Ques)

9. Demand for electricity has increased. However, supply cannot be increased due to lack of resources.

Explain how, in any two ways, demand for electricity can be decreased. Also identify the value being

highlighted in the above question.

10. What economic measures can the government take to reduce demand for commodity X which is harmful

for health?

Unit III : Producer‟s Behaviour & Supply

Chapter 5 : Production (1 Mark Ques)

1. Explain the concept of production function.

2. Give meaning of “Return to a Factor”.

3. Define law of variable proportion.

4. TRUE or FALSE – (i) When TP is constant AP will fall

(ii) TP increase only when MP increases

(iii) If MP falls, AP also falls.

(iv) Increase in TP always indicates that these are increasing returns to a factor.

5. What is the Average Product of an input?

(3 – 4 Mark Ques)

6. Distinguish between short-run & long run production function.

7. State the relation between AP & MP. Use diagram.

8. Complete the following table.

Units of Labour AP (units) MP (units)

1

2

3

4

5

6

8

10

-

9

-

7

-

-

10

-

4

-

9. Explain the changes that takes place in TP & MP under increasing returns to a factor.

10. Explain the likely behaviour of TP & MP when for increasing production only one input is increased while

all other inputs are kept constant.

Price / unit (Rs) Demand (units)

9 100

9 150



(6 Marks Ques)

11. Explain the law of variable proportion through the behaviour of TP & MP. Give reason behinal each phase.

Use diagram.

Chapter 6 : COST

(1 Mark Ques)

1. How does TFC change when output changes.

2. Why does AFC fall with increase in output

3. What is the relation between AVC & ATC, if AFC is zero?

4. TRUE or FALSE (i) AC falls only when MC falls.

(ii) When MC rises, AC will also rise.

(iii) TC rises only when MC rises.

(iv) AVC can fall even when MC is rising.

5. AFC curve is a rectangular hyperbola curve. YES or NO. Give reason.


6. Justify the statement, In economics, normal profits are always part of TC:

7. Distinguish between explicit cost & implicit cost. Give example of each.

8. What is the behaviour of (a) Average Fixe Cost & (b) Average Variable Cost as more & more units of a

good are produced?

9. Draw TVC, TC, & TFC curves in a single diagram.

10. Relationships between : (i) AC & MC (ii) TC & MC (iii) MC & AVC

11. Why does difference between ATC & AVC decreases with increase in level of output? Explain.

12. Complete the following table:

Output (units) TC (Rs) AVC (Rs) MC (Rs) AFC (Rs)

0 30

1 - - 25 30

2 78 - - -

3 - 23 - 10

4 - - 23 -

5 150 - - 6

Chapter 7 : SUPPLY

(1 Mark Ques)

1. What is „increase‟ & „decrease‟ in supply.

2. Price elasticity of supply of a good is 0.8. Is the supply „elastic‟ or „Inelastic‟ and why?

3. Difference between stock & supply.

4. When is the supply of a commodity called „Inelastic‟.

5. What causes an upward movement along the supply curve of a commodity.




6. What is meant by the assumption, „other things remaining the same‟ on which law of supply is based?

7. Under what condition, a producer would like to supply more at a given level of price?

8. Explain the effect of technological advancement, on supply of a product.

9. Differentiate between „Increase in Supply‟ and Expansion in Supply‟.

10. What would be an effect on supply curve of the following:

(a) Decrease in tax on product.

(b) Subsidy on production of goods.

(c) Rise in own price of a good.

11. The price of a commodity is Rs 12 per unit & its quantity supplied is 500 units. When its price rises to

Rs 15/ unit, its quantity supplied rises to 650 units, calculate its price elasticity of supply. Is the supply

elastic?

12. From the following data, calculate elasticity of supply.

Price (per unit) (Rs) 5 6

Total Revenue 100 156

13. Distinguish between „Change in Supply‟ & „Change in Quantity Supplied‟.

Chapter 8 : REVENUE

(1 Mark Ques)

1. Comment on the shape of the MR curve in case the TR is a horizontal straight line.

2. What is the behaviour of AR n a market in which a firm can sell more only by lowering the price?

3. What is the behaviour of AR in a market in which a firm can sell any quantity of the output it produces at a

given price?


4. A producer can sell any quantity of output of the good he produces at a given prices. Prepare a TR & MR

schedule for four output levels.


6. Explain the relation between MR & AR when a firm is able to sell more quantity of output:

(i) at the same price

(ii) only by lowering the price

7. What is Revenue of a firm? Give meaning of AR & MR. What happens to AR when MR is:

(i) greater than AR

(ii) equal to AR

(iii) less than AR

Output Price TR MR

4

5

6

7

8

9

-

-

6

-

36

-

42

-

40

-

4

-

-

-



Chapter 9 : PRODUCER EQUILIBRIUM

(1 Mark Ques)

1. Explain producer‟s equilibrium.


2. Hiring reasons identify the equilibrium level of output and find profit at this output using „MC & MR

approach‟ from the following:

Output 1 2 3 4 5

TR (Rs) 8 15 21 26 30

TC (Rs) 8 13 19 27 36

3. Explain the producer‟s equilibrium with MR / MC approach (when price remains constant with the rise in

output).

4. Explain producer‟s equilibrium with MR / MC approach (when price falls with rise in output).

5. Is a producer‟s equilibrium under the following situations?

(i) when MR > MC (ii) when MR = MC (iii) when MR < MC

UNIT – IV : Forms of Market and Price Determination under

perfect competition with simple applications

Chapter 10 : Perfect Competition

(1 Mark Ques)

1. What is meant by the term „ price taker‟ in the context of a firm?

2. What induces new firms to enter an industry?

3. Under which market form MR of a firm does not change?

4. In which market form does a firm face perfectly elastic demand curve.

5. What is the effect on price when a perfectly competitive firm tries to sell more?


6. Explain feature of homogeneous product.

7. Explain feature of perfect knowledge about the market.

(6 Marks Ques)

8. Explain implications of the following features of a perfectly competitive market:

(i) Large number of buyers & sellers.

(ii) Freedom of entry & exit.

Chapter 11 : NON – COMPETITIVE MARKET

(1 Mark Ques)

1. What is a price maker firm.

2. Give meaning of : (i) Monopoly (ii) Monopolistic competition (iii) Oligopoly

3. Why is AR (demand curve) under monopolistic competition is more elastic than AR curve under monopoly.

4. Why is AR curve of a firm negatively sloped under monopolistic competition? Explain.



5. Name the characteristic which makes monopolistic competition different from perfect competition.

(3 – 4 Marks)

6. Explain the feature of firms mutually Interdependent in an oligopoly market.

7. Discuss the primary reason for „Indeterminateness of demand curve‟ under the oligopoly form of market.

8. Distinguish between perfect and imperfect oligopoly.

9. Ambuja, Ultra-Tech, ACC, JP cement are only a few cement producers in Indian market. Identify the form

of market in which they sell their products & also explain its features. If they decide to form collusive

oligopoly, then which value is being violated by them?

10. Explain 2 sources of restricted entry under monopoly.

Chapter 12 : Market Equilibrium with simple Applications

(1 Marks Ques)

1. Meaning of equilibrium price.

2. Suggest any one economic measure by which the government can promote consumption of „Khadi‟.

3. What happens to equilibrium price of a commodity if there is „decrease‟ in its demand and „increase‟ in its

supply.

4. What economic measure can the government take to reduce demand for a commodity which is harmful for

health?


5. Explain „black marketing‟ as a direct consequence of price ceiling.

6. Explain the concept of „buffer stock‟ as a tool of price floor.

7. Market is in equilibrium. Explain the chain of reactions in the market if the price is:

(i) higher than equilibrium price.

(ii) lower than equilibrium price.

8. If at a given price of the commodity there is excess demand, how will the equilibrium price be reached?

Explain with the help of a diagram.

9. Market for a good is in equilibrium. There is increase in demand for goods. Explain the chain of effects of

this change. Use diagram.

10. Explain the affects of „Price Ceiling‟ & „Price Floor‟.



Name: _____________ Subject: Macro - Economics Class: XII C

PART – B

Unit V : National Income & Related Aggregates Chapter – 1 : Introduction to Macro-Economics and its concepts

(1 Marks Ques)

1. Define stocks & flow.

2. Define intermediate and final goods.

3. TRUE or FALSE : (i) Capital formation is a flow

(ii) Bread is always a consumer good.


4. Distinguish between consumer goods & capital goods which of these are final goods.

5. Define intermediate goods and final goods. Can milk be an intermediate goods? Give reason for your

answer.

6. Explain the circular flow of income.

Chapter 2 : National Income and Related Aggregates

(1 Marks Ques)

1. What are „subsidies‟?

2. What is meant by „consumption of fixed capital‟?

3. Define capital formation.

(3 – 4 Marks)

4. Differentiate between domestic income (NDPfc) Vs National Income (NNPfc) .

5. What are externalities. Give examples of positive & negative externalities & its impact on welfare of the

people.

6. Explain how „Non-Monetary Exchanges‟ are a limitation in taking GDP as an index of welfare.

7. What is real GDP? State 3 limitations of GDP as an index of economic welfare.

8. Calculate Gross Fixed Capital formation from the following data:

Ans: GDFCF = 1150 crore

9. Calculate „Value of Output‟ from the following data.

Ans: GVAMP 125 lakh value of o/p = 200

Particulars Amount

(i) Private final consumption expenditure 1000

(ii) Government final consumption exp. 500

(iii) Net exports (-) 50

(iv) Net factor income from abroad 20

(v) Gross domestic product at MP 2500

(vi) Opening stock 300

(vii) Closing stock 200

(i) NVA at FC 100 Lakhs

(ii) Intermediate consumption 75

(iii) Excise duty 20

(iv) Subsidy 5

(v) Depreciation 10



10. Calculate GVA at FC

Particulars Rs. in crores

(i) Units of output sold (units) 1000

(ii) Price per unit of output 30

(iii) Depreciation 1000

(iv) Intermediate cost 12000

(v) Closing stock 3000

(vi) Opening stock 2000

(vii) Excise duty 2500

(viii) Sales Tax 3500

Ans: GVAMP = 19000 GVAFC = 13000 crores

11. Calculate „sales‟ from the following data:

(i) Subsidies 200

(ii) Opening stock 100

(iii) Closing stock 600

(iv) Intermediate consumption 3000

(v) Consumption of fixed capital 700

(vi) Profit 750

(vii) Net value added at FC 2000

Ans: GVAMP = 2500 lakhs Sales = 5000

12. Calculate GNP at FC from the following data by : (i) Income Method (ii) Expenditure Method

Ans : NDPFC = 1600 crore

GNPFC = 1650 crore

GDPMP = 1740

GNPFC = 1650

(i) PFCE 1000

(ii) NDCF 200

(iii) Profits 400

(iv) COE 800

(v) Rent 250

(vi) GFCE 500

(vii) Depn 60

(viii) Interest 150

(ix) Net current transfer from rest of the world (-80)

(x) Net factor income from abroad (-10)

(xi) Net exports (-20)

(xii) NIT 80



13. Calculate (a) GDP at MP and (b) Factor income from abroad

(i) Profit 500 (in „000 crores)

(ii) Export 40

(iii) COE 1500

(iv) GNP at FC 2800

(v) Net current transfer from rest of the world 90

(vi) Rent 300

(vii) Interest 400

(viii) Factor income to abroad 120

(ix) NIT 250

(x) Net domestic capital formation 650

(xi) Gross fixed capital formation 700

(xii) Change in stock 50

Ans: NDPFC = 2700

depn = 150

GDPMP = 3100

NFIA = -50

14. Calculate National Income by the Expenditure Method:

(i) GVA at MP by primary sector 300 (crores)

(ii) PRCE 750

(iii) consumption of fixed capital 150

(iv) NIT 20

(v) GVA at MP by secondary sector 200

(vi) NDFCF 220

(vii) Change in stock (-) 20

(viii) GVA at MP by tertiary sector 700

(ix) Net Imports 50

(x) GFCE 150

(xi) Net factor Income from abroad 20

Ans: GDPMP = 1200 crores

NNPFC = 1050



15. Calculate National Income (i) Income method (ii) expenditure method

(i) GFCE 2000

(ii) NDCF 600

(iii) Consumption of fixed capital 70

(iv) Net exports 60

(v) NIT 200

(vi) PFCE 4000

(vii) Net factor income to abroad 60

(viii) COE 3660

(ix) Profit 1500

(x) Rent 500

(xi) Interest 800

(xii) Dividend 300

Ans : NDPFC = 6460 crores

NNPFC = 6400

GDPMP = 6730

NNPFC = 6400

UNIT : VI – MONEY AND BANKING

Chapter : 3 – Money and Banking

(1 Mark Ques)

1. Define legal Reserve Ratio.

2. State the components of supply of money.

3. What is meant by statutory liquidity ratio.

4. What will be the effect of a rise in bank rate on the money supply?

5. What is commercial bank & central bank?


6. Explain the „banker to the government‟ function of the central bank.

7. What role of RBI is known as „Lender of Last resort‟ function of the central bank.

8. Explain any two methods of credit control used by central bank.

9. What is bank rate policy? How does it work as a method of credit control?

10. What is meant by open market operation? How does it reduce the money supply in the economy.

UNIT : VII – DETERMINATION OF INCOME AND EMPLOYMENT

Chapter : 4 – Aggregate Demand and its Related concepts

(1 Marks Ques)

1. Why can value of MPC be not greater than one?

2. Can the value of average propensity to save to be negative? If yes, when?

3. Give the meaning of automonous consumption.

4. Name any 2 components of Aggregate Demand.




5. Explain the distinction between „Autonomous consumption‟ and „Induced consumption‟.

6. “Economists are generally concerned about the rising MPS in an economy”. Explain why.

7. On the basis of consumption function C = 100 + 0.754. Answer the following question:

(i) Derive the saving function.

(ii) Determine the saving at the income level of 1000 crore.

(iii) At what level of income, saving becomes zero?


9. Derive a straight line saving curve using the following consumption function C = 200 + 0.64 Presuming the

income levels to be Rs 100, Rs 200 & Rs 300 crores. Also calculate that level of income where consumption

is equal to income.

10. Given below is the consumption function of an economy: C = 100 + 0.54 with the help of a numerical

example show that in this economy as income increases, APC will decrease.

Chapter : 4 – National Income Determination and Multiplier

(1 Marks Ques)

1. Give the meaning of ex-ante savings.

2. If MPS is 0.1, calculate the value of multiplier.

3. If investment multiplier is 1, what will be the value of MPC?

4. What is the value of multiplier when MPC & MPS are equal?


5. Explain the distinction between ex-ante measures & ex-post measures.

6. C = 50 + 0.54 is the consumption function, where C is consumption expenditure & 4 is national income, and

investment expenditure is Rs 2000 in an economy. Calculate:

(i) Equilibrium level of national income

(ii) Consumption expenditure at equilibrium level of national income.

7. Find national income from the following data:

8. Final „investment‟ from the following: National Income Rs 500 , Autonomous consumption Rs 100,

MPC = 0.75.

9. In a two-sector economy the saving & investment function are:

S = -20 + 0.44

I = -5 + 0.24

What will be the equilibrium level of income?

10. An increase of Rs 250 crore in investment in an economy resulted in total increase in income of Rs 1000

crore. Calculate the following:

(a) MPC

(b) Change in saving

(c) Change in consumption expenditure

(d) Value of multiplier.

Income Consumption MPS APS

0

50

100

150

40

70

100

120

-

-

-

-

-

-

-

-



11. An economy is in equilibrium from the following data, calculate autonomous consumption

(i) Income = 10,000

(ii) MPC = 0.9

(iii) Autonomous consumption = 100

Chapter : 6 – EXCESS DEMAND AND DEFICIENT DEMAND

(1 Marks Ques)

1. Define Deflationary & Inflationary gap.

2. Give meaning of excess & deficient demand.

3. What do you mean by full employment.


4. What is meant by Margin Requirement? How does the central bank use this measure to control deflationary

conditions in an economy?

5. Explain the meaning of underemployment equilibrium. Explain 2 measures by which full employment

equilibrium can be reached.

6. Explain the concept of „inflationary gap‟. Also explain the role of „legal reserves‟ in reducing it.

7. Explain the concept of „deflationary gap‟ & the role of open market operations in reducing this gap.

8. Explain the situation of „Excess demand‟ & „Deficient demand‟. Also explain the role of „Reverse Repo

Rate‟ & „Repo Rate‟ in correcting it.

UNIT : VIII – GOVERNMENT BUDGET AND THE ECONOMY

Chapter : 7 – Government Budget and the Economy

(1 Mark Ques)

1. Define government budget with its objectives.

2. Name any one step taken by government through budget to reduce the gap between the rich & the poor.

3. Give 2 examples of Revenue Receipt & Capital Receipt.

4. Define fiscal deficit & Primary deficit.

5. Distinguish between direct tax & indirect tax.


6. Explain the allocation function of a government budget.

7. Explain how the government can use the budgetary policy in reducing inequalities of incomes.

UNIT : IX – BALANCE OF PAYMENTS

Chapter : 8 – Foreign Exchange Rate

1. What are the functions of foreign exchange market?

2. Why does demand for foreign exchange rise when its price falls.

3. Why does a rise in foreign exchange rate cause a rise in foreign exchange supply?

4. How can increase in FDI affects the price of foreign exchange.

5. Explain effect of depreciation of domestic currency on exports.

6. If Government of India raise the import duty. What impact is it likely to have on foreign exchange rate

& how?

7. Differentiate between fixed exchange rate and flexible exchange rate.

8. What is the role of a central bank in the following exchange rate?

(a) Fixed exchange

(b) Floating exchange

(c) Managed floating



Chapter : 9 – Balance of Payment

1. Differentiate between „Balance of Trade‟ and „Balance of Payment‟.

2. What does Balance of Payments account show? Name the two parts of the balance of payments account.

3. What do you mean be Capital Accounts and what are is components?

4. Where is „borrowings from abroad‟ recorded in the balance of payments accounts? Give reason.

5. What is meant by „official‟ reserve transactions‟? Discuss their importance in BOP.

6. Distinguish between autonomous & accommodating transactions of BOP account.

7. What will be the effect of foreign investments in India on exchange rate? Explain.

8. In which sub-account & on which side of BOP account will foreign investments in India be recorded? Give

reasons.

Bhartiyam International School Subject: Business Studies

Class: XII (C)

Chapter 1 Nature and significance of Management

1. State any three organisational objectives of Management.

2. What is meant by management as an science. Explain with the help of any three features.

3. Explain any three points of importance of coordination.

4. Explain any four points that highlight the importance of Management.

5. Coordination is the essence of management. Explain. How?

Chapter 2 Principles of management

1. What is meant by principles of management?

2. State the role of speed boss in functional foremanship.

3. What is the objective of method study as a technique of scientific management.

4. State any four features of principles of management.

5. Explain briefly ‘initiative’ and ‘esprit de corps’ as principles of general management.

6. Explain briefly ‘remuneration of employees’ and ‘scalar chain’ as principles of general

management.

7. Explain the technique of scientific management which separates the planning and execution

work.

8. Principles of Taylor and Fayol can come in the form of case study.

Chapter 3 Business environment

1. Define liberalisation as a process of economic reforms.

2. Explain any two impacts of government policy changes on business and industry.

3. State any five features of business environment.

4. Demonetisation is the act of stripping or discontinuing a currency unit of its status as legal.

Why does demonetisation policy implement in a country?

5. Write a limitation of demonetisation.

6. Questions related to dimensions of business environment and features can come in form of

case study?

Chapter 4 Planning

1. Name the type of plan which tells what is to be done and what is not to be done.

2. Name the type of plan which defines the parameters in which a manager can function.

3. Name the type of plan which provides the broad contours of an organisation's business.

4. State any three features of planning.

5. How does planning leads to rigidity and reduce creativity. Explain.

6. Define planning. State any four points of importance of planning.

7. Process of planning can come in form of case study.

Chapter 5 Organising

1. Name the type of organisational structure which promotes efficiency and utilisation of

manpower.

2. Differentiate between formal and informal organisation on the basis of flow of

communication.

3. Give the meaning of authority as an element of delegation

4. What is meant by divisional structure of organisation. State it’s any three advantages.

5. Explain by giving any three reasons why delegation is important in an organisation.

6. State any Four Points of importance of organising as a function of management.

7. Process of organising can come in form of case study.

Chapter 6 Staffing

1. Name the method of training in which trainees learn on the equipment they will be using.

2. Name the method of training in which the trainee works directly with the senior manager

and the manager takes full responsibility of the training.

3. Name the method of training in which the trainee learns under the guidance of a master

worker.

4. Why is training important for the employees. State any three reasons.

5. Internal sources of recruitment are better than external sources of recruitment. Explain by

giving reasons in support of the statement.

6. How is training of employees beneficial for the organisation? State by giving any four

reasons.

7. Process of staffing is important from the point of view of case study.



Super 30 Questions of Physical Education

Class XII Q. 1 What do you mean by seeding?

Q.2 What do you mean by Bye?

Q. 3 Prepare a knock-out fixture of 17 teams

Q. 4 What do you mean by intramural and extramural activities

Q. 5 What do you mean by specific sports programme ? explain such 3 programme

Q.6 What do you mean by food intolrance?

Q.7 Explain the nutritive components of diet

Q.8 Explain water and fat soluable vitamins in detail

Q.9 What do you mean by food supplement ?

Q.10 Explain the effect of diet on performance

Q.11 Explain five liife style disease in detail

Q.12 Explain different types of disability

Q.13 Explain different types of disorder in detail

Q.14 What do you mean by gross and fine motor skill

Q.15 What is weight training ? explain the advantages of weight tranning

Q.16 Explain five postural deformities in detail

Q.17 Explain psychological and sociological aspects of women participation in sports

Q.18 Explain women athletes triad in detail

Q.19 Explain the procedure of harvard step test in detail

Q.20 Explain all the items of AAPHER test in detail

Q.21 Explain the effects of exercises on circulatory, respiratory and muscular system in detail

Q.22 Explain the anatomical and physiological differeces between male and female

Q.23 Explain all the soft tissue and hard tissue injuries in detail

Q.24 What is projectile? What are the various factors affecting projectile trejetory ?



Q.25 Discuss about the muscules which involves in running,thorowing and jumping

Q.26 Explain the problem focused and emotion focused cooping strategies in detail

Q.27 What is motivation ? explain the technique of motivation

Q.28 Explain the strength and endurance developing training method in detail

Q.29 Discuss the different types of coordinative activities in detail

Q.30 Prepare a circuit training diagram and also discuss the load increasing procedure of circuit

training in detail



Name: ______ Subject: Mathematics Class: XII

Chapter 1- Relation and Function

1. If a*b = a + b + ab on Z , find the identity of *.

2. Let A = { 1,2,3,4}. Let R be the equivalence relation on A X A define by (a,b) R (c,d) such that a +

d = b +c. Find the equivalence class [ (1,3)].

3. Show that the relation R in the set A = 𝑥 ∈ 𝑍: 0 ≤ 𝑥 ≤ 12 , given by R =

𝑎, 𝑏 : 𝑎 − 𝑏 𝑖𝑠 𝑎 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑜𝑓 4 is a equivalence relation. Find the set of all element s related to

1.

4. Consider ƒ ∶ 𝑅+ → [ -5, ∞ ) given by ƒ 𝑥 = 9𝑥2 + 6x -5. Show that ƒ is invertible . Hence find inverse

of ƒ .

5. Define a binary operation * on the set { 0,1,2,3,4,5 } as

a*b = a + b

a + b − 6,

if a + b < 6if A + b ≥ 6

Show that zero is the identity for this operation and each element a of the set is

invertible with 6 – a being the inverse of a.

6. Find 𝑔𝑜ƒ(2) if ƒ(x) = 2x-3 and g(x) = 𝑥2 − 8 .

7. Show that, if f: R – 7

5 → R -

3

5 is define by f(x) =

3𝑥+4

5𝑥−7 and g : R −

3

5 → R -

7

5 is define by g(x)

= 7𝑥+4

5𝑥−3, then fog = 𝐼𝐴 and gof = 𝐼𝐵 ,where 𝐼𝐴 and 𝐼𝐵 are the identity functions on sets A and B. Hence

find 𝑓−1 (x) and 𝑔−1 (x) .

8. Let ƒ ∶ N→ N be define by ƒ 𝑛 =

n+1

2 ,

n

2,

if n is oddif n is even

∀ n∈ N.

State whether the function ƒ is bijective. Justify your answer

9. Let * be a binary operation defined on Q Q by a, b c, d ac, b ad , where Q is the set of

rational numbers. Determine, whether * is commutative and associative. Find the identity element

for * and the invertible elements of Q Q .

10. Let N denote the set of all natural number and R be the relation on N×N define by

(a, b) R (c, d) if ad(b + c) = bc( a + d). Show that R is transitive.

Chapter 2- Inverse Trigonometric Function

11. Find the value of sin( cot−1 a + tan−1 𝑎 ).

12. Solve : sin−1 𝑥 + sin−1(1 − 𝑥) = cos−1 𝑥 .

13. Proved that cot−1 1+sin 𝑥 + 1−sin 𝑥

1+sin 𝑥− 1−sin 𝑥 =

𝑥

2 , x ∈ 0,

𝜋

4 .

14. If sin sin−1 1

5 + cos−1 𝑥 = 1, find the value of x.

15. If tan−1 𝑎 + tan−1 𝑏 + tan−1 𝑐 = 𝜋 , then prove that a + b + c = abc

16. Solve: cos(tan−1 𝑥) = sin(cot−1 3

4 ).

17. Solve for x : tan-1

𝑥 − 1

𝑥 − 2 + tan

-1

𝑥 + 1

𝑥 + 2 =

𝜋

4 .



18. Prove that : sin-1

12

13 + cos

-1

4

5 + tan

-1

63

16 = 𝜋 .

19. Show that: tan 1

2 𝑠𝑖𝑛−1

3

4 =

4 − 7

3 .

20. Write the principal value of tan-1

(1) + sec-1

(2) + sin-1

(sin5𝜋/4).

21. If cos−1 𝑥

𝑎+ cos−1 𝑦

𝑏= 𝛼 , proved that

𝑥2

𝑎2 – 2 𝑥𝑦

𝑎𝑏 cos𝛼 +

𝑦2

𝑏2 = sin 2𝛼.

Chapter 3- Matrices

22. The bookshop of school A and B has 10 dozen chemistry books, 8 dozen physics

books , 10 dozen mathematics books and 8 dozen chemistry books, 10 dozen

physics books , 12 dozen mathematics books respectively. Their selling prices are

Rs. 80 , Rs. 60 and Rs. 40 each respectively. Find the total amount the

bookshoop will receive from selling all the books using matrix algebra.

23. Find a matrix X such that X 1 2 34 5 6

= −7 −8 −92 4 6

24. Using elementary transformation, find the inverse of the matrix

2 0 −15 1 00 1 3

25. Write the number of possible matrices of order 3 x 3 with each entry 1,2 or 3.

26. Matrix A = 0 2𝑏 −23 1 3

3𝑎 3 −1

is given to be symmetric, find the values of a and b.

27. If A = 3 −24 −2

and I = 1 00 0

, find k such that 𝐴2 = k A – 2I.

28. If A = 4 56 7

, then find the det(𝐴𝑇).

29. Find the inverse of the matrix A= 𝑎 𝑏

𝑐1+𝑏𝑐

𝑎

and show that a A-1

= (a2 + bc + 1) I – a A.

30. Suppose A = 2 2 1−2 1 21 −2 2

and B = 1 3 21 1 12 −3 1

, verify that (AB)-1

= B-1

A-1

.

Chapter 4- Determinants

31. If 𝐴 = −3 0 5 6 1 0−2 0 1

. What is the value of 𝑎11𝐴12 + 𝑎32𝐴31 .

32. If adj A = 16, of a matrix order 3 x 3, then find 𝐴 .



33. A trust invested some money in two types of bonds .The first bond pays 10% interest

and second bond pays 12% interest. The trust received Rs. 2,800 as interest. However,

if trust had interchanged money in two bonds, they would have got Rs. 100 less as

interest. Using matrix method, find the amount invested by the trust. Interest received

on this amount will be given to Helpage India as donation. Which value is reflected in

this question ?

34. Using properties of determinants, show that ∆ABC is isosceles, if

1 1 1

1 + sin 𝐴 1 + sin 𝐵 1 + 𝑠𝑖𝑛𝐶𝑠𝑖𝑛2𝐴 + sin 𝐴 𝑠𝑖𝑛2𝐵 + sin 𝐵 𝑠𝑖𝑛2𝐶 + sin 𝐶

= 0

35. Using properties of determinants, prove the following:

x x + y x + 2y

x + 2y x x + yx + y x + 2y x

= ay2 ( x+ y) .

36. Using product 1 −1 20 2 −33 −2 4

−2 0 1 9 2 −3 6 1 −2

to solve the system of following

equations :

x – y + 2 z = 1 ; 2y – 3 z = 1; 3x – 2y + 4z = 2 .

37. If adj A = 16 of a matrix order 3 x 3, then find 3𝐴 .

38. Evaluate: 𝑥 + 4 2𝑥 2𝑥

2𝑥 𝑥 + 4 2𝑥2𝑥 2𝑥 𝑥 + 4

= 0 ,using properties of determinants.

39. For what value of k 𝜖 N, 𝑘 −43 −𝑘

is singular.

40. Using property of determinants, show that

𝑎2 𝑏𝑐 𝑐2 + 𝑎𝑐

𝑎2 + 𝑎𝑏 𝑏2 𝑎𝑐𝑎𝑏 𝑏2 + 𝑏𝑐 𝑐2

= 4𝑎2𝑏2𝑐2

Chapter 5- Continuity and Differentiability

41. For what value of 𝜆 is the function define by

ƒ 𝑥 = { 𝜆 𝑥2 − 2𝑥 𝑖𝑓 𝑥 ≤ 0

4𝑥 + 1 𝑖𝑓 𝑥 > 0

continuous at x = 0 ? What about continuity at x = 1.



42. Prove that f(x) = 𝑥 + 1 , is not differentiable at x = 1.

43. Discuss the continuity of ƒ 𝑥 = { 𝑠𝑖𝑛𝑥 − 𝑐𝑜𝑠𝑥 , 𝑥 ≠ 0 −1 , 𝑥 = 0 .

44. Differentiate: 𝑥𝑥 cos 𝑥 + 𝑥2+1

𝑥2−1

45. If x 1 + 𝑦 + y 1 + 𝑥 = 0 , proved that 𝑑𝑦

𝑑𝑥 = -

1

(𝑥+1)2 .

46. If x = a ( cos 𝑡 + t sin 𝑡 ) and y = a ( sin 𝑡 - t cos 𝑡 ), find 𝑑2𝑦/ 𝑑𝑥2.

47. If y = ( tan−1 𝑥)2 , show that ( 𝑥2 + 1 )2 𝑦2 + ( 𝑥2 + 1) 𝑦1 = 2 .

48. Differentiate: 𝑐𝑜𝑠 𝑥3 . 𝑠𝑖𝑛2𝑥2.

49. If y = sin−1 𝑥, then prove that ( 1- 𝑥2 )𝑑2𝑦

𝑑𝑥 2 - x 𝑑𝑦

𝑑𝑥 = 0

50. Differentiate: 𝑥2 + xy – sin 𝑥𝑦 = 0

Chapter 6- Application of Derivatives

51. Find the approximate value of 0.009 3

using derivative.

52. What will be the change in surface area of a cube if its edge is decreasing by 3%.

53. Find the equation of normals to the curve y = 𝑥3 + 2x + 6 which are parallel to the line

x + 14y + 4 = 0 .

54. The sum of the perimeter of a circle and a square is k, where k is some constant. Prove

that the sum of their areas is least when the side of square is double the radius of the

circle.

55. Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is

8/27 of the volume of the sphere.

56. Find the intervals in which ƒ(x) = 2 𝑥3 – 3 𝑥2 – 36 𝑥 + 7 is strictly increasing or

decreasing. Also find the maximum and minimum value of ƒ(x).

57. Find a point on the curve y = 𝑥 − 2 2 at which the tangents is parallel to the chord joining the point

( 2,0) and ( 4,4).

58. For the curve y = 4𝑥3 - 3 𝑥5, find the all points at which the tangents passes through the origin.

59. Prove that the curves x = 𝑦3 and xy = k cut at right angle if 8𝑘3 = 1.

60. Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of

height h and semi vertical angle 𝛼 is one third that of the cone and the greatest volume of cylinder is

4

27 𝜋 𝑕3 𝑡𝑎𝑛2𝛼



Name: ______ Subject: Mathematics Class: XII

Chapter 1- Relation and Function

1. If a*b = a + b + ab on Z , find the identity of *.

2. Let A = { 1,2,3,4}. Let R be the equivalence relation on A X A define by (a,b) R (c,d) such that a +

d = b +c. Find the equivalence class [ (1,3)].

3. Show that the relation R in the set A = 𝑥 ∈ 𝑍: 0 ≤ 𝑥 ≤ 12 , given by R =

𝑎, 𝑏 : 𝑎 − 𝑏 𝑖𝑠 𝑎 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑜𝑓 4 is a equivalence relation. Find the set of all element s related to

1.

4. Consider ƒ ∶ 𝑅+ → [ -5, ∞ ) given by ƒ 𝑥 = 9𝑥2 + 6x -5. Show that ƒ is invertible . Hence find inverse

of ƒ .

5. Define a binary operation * on the set { 0,1,2,3,4,5 } as

a*b = a + b

a + b − 6,

if a + b < 6if A + b ≥ 6

Show that zero is the identity for this operation and each element a of the set is

invertible with 6 – a being the inverse of a.

6. Find 𝑔𝑜ƒ(2) if ƒ(x) = 2x-3 and g(x) = 𝑥2 − 8 .

7. Show that, if f: R – 7

5 → R -

3

5 is define by f(x) =

3𝑥+4

5𝑥−7 and g : R −

3

5 → R -

7

5 is define by g(x)

= 7𝑥+4

5𝑥−3, then fog = 𝐼𝐴 and gof = 𝐼𝐵 ,where 𝐼𝐴 and 𝐼𝐵 are the identity functions on sets A and B. Hence

find 𝑓−1 (x) and 𝑔−1 (x) .

8. Let ƒ ∶ N→ N be define by ƒ 𝑛 =

n+1

2 ,

n

2,

if n is oddif n is even

∀ n∈ N.

State whether the function ƒ is bijective. Justify your answer

9. Let * be a binary operation defined on Q Q by a, b c, d ac, b ad , where Q is the set of

rational numbers. Determine, whether * is commutative and associative. Find the identity element

for * and the invertible elements of Q Q .

10. Let N denote the set of all natural number and R be the relation on N×N define by

(a, b) R (c, d) if ad(b + c) = bc( a + d). Show that R is transitive.

Chapter 2- Inverse Trigonometric Function

11. Find the value of sin( cot−1 a + tan−1 𝑎 ).

12. Solve : sin−1 𝑥 + sin−1(1 − 𝑥) = cos−1 𝑥 .

13. Proved that cot−1 1+sin 𝑥 + 1−sin 𝑥

1+sin 𝑥− 1−sin 𝑥 =

𝑥

2 , x ∈ 0,

𝜋

4 .

14. If sin sin−1 1

5 + cos−1 𝑥 = 1, find the value of x.

15. If tan−1 𝑎 + tan−1 𝑏 + tan−1 𝑐 = 𝜋 , then prove that a + b + c = abc

16. Solve: cos(tan−1 𝑥) = sin(cot−1 3

4 ).

17. Solve for x : tan-1

𝑥 − 1

𝑥 − 2 + tan

-1

𝑥 + 1

𝑥 + 2 =

𝜋

4 .



18. Prove that : sin-1

12

13 + cos

-1

4

5 + tan

-1

63

16 = 𝜋 .

19. Show that: tan 1

2 𝑠𝑖𝑛−1

3

4 =

4 − 7

3 .

20. Write the principal value of tan-1

(1) + sec-1

(2) + sin-1

(sin5𝜋/4).

21. If cos−1 𝑥

𝑎+ cos−1 𝑦

𝑏= 𝛼 , proved that

𝑥2

𝑎2 – 2 𝑥𝑦

𝑎𝑏 cos𝛼 +

𝑦2

𝑏2 = sin 2𝛼.

Chapter 3- Matrices

22. The bookshop of school A and B has 10 dozen chemistry books, 8 dozen physics

books , 10 dozen mathematics books and 8 dozen chemistry books, 10 dozen

physics books , 12 dozen mathematics books respectively. Their selling prices are

Rs. 80 , Rs. 60 and Rs. 40 each respectively. Find the total amount the

bookshoop will receive from selling all the books using matrix algebra.

23. Find a matrix X such that X 1 2 34 5 6

= −7 −8 −92 4 6

24. Using elementary transformation, find the inverse of the matrix

2 0 −15 1 00 1 3

25. Write the number of possible matrices of order 3 x 3 with each entry 1,2 or 3.

26. Matrix A = 0 2𝑏 −23 1 3

3𝑎 3 −1

is given to be symmetric, find the values of a and b.

27. If A = 3 −24 −2

and I = 1 00 0

, find k such that 𝐴2 = k A – 2I.

28. If A = 4 56 7

, then find the det(𝐴𝑇).

29. Find the inverse of the matrix A= 𝑎 𝑏

𝑐1+𝑏𝑐

𝑎

and show that a A-1

= (a2 + bc + 1) I – a A.

30. Suppose A = 2 2 1−2 1 21 −2 2

and B = 1 3 21 1 12 −3 1

, verify that (AB)-1

= B-1

A-1

.

Chapter 4- Determinants

31. If 𝐴 = −3 0 5 6 1 0−2 0 1

. What is the value of 𝑎11𝐴12 + 𝑎32𝐴31 .

32. If adj A = 16, of a matrix order 3 x 3, then find 𝐴 .



33. A trust invested some money in two types of bonds .The first bond pays 10% interest

and second bond pays 12% interest. The trust received Rs. 2,800 as interest. However,

if trust had interchanged money in two bonds, they would have got Rs. 100 less as

interest. Using matrix method, find the amount invested by the trust. Interest received

on this amount will be given to Helpage India as donation. Which value is reflected in

this question ?

34. Using properties of determinants, show that ∆ABC is isosceles, if

1 1 1

1 + sin 𝐴 1 + sin 𝐵 1 + 𝑠𝑖𝑛𝐶𝑠𝑖𝑛2𝐴 + sin 𝐴 𝑠𝑖𝑛2𝐵 + sin 𝐵 𝑠𝑖𝑛2𝐶 + sin 𝐶

= 0

35. Using properties of determinants, prove the following:

x x + y x + 2y

x + 2y x x + yx + y x + 2y x

= ay2 ( x+ y) .

36. Using product 1 −1 20 2 −33 −2 4

−2 0 1 9 2 −3 6 1 −2

to solve the system of following

equations :

x – y + 2 z = 1 ; 2y – 3 z = 1; 3x – 2y + 4z = 2 .

37. If adj A = 16 of a matrix order 3 x 3, then find 3𝐴 .

38. Evaluate: 𝑥 + 4 2𝑥 2𝑥

2𝑥 𝑥 + 4 2𝑥2𝑥 2𝑥 𝑥 + 4

= 0 ,using properties of determinants.

39. For what value of k 𝜖 N, 𝑘 −43 −𝑘

is singular.

40. Using property of determinants, show that

𝑎2 𝑏𝑐 𝑐2 + 𝑎𝑐

𝑎2 + 𝑎𝑏 𝑏2 𝑎𝑐𝑎𝑏 𝑏2 + 𝑏𝑐 𝑐2

= 4𝑎2𝑏2𝑐2

Chapter 5- Continuity and Differentiability

41. For what value of 𝜆 is the function define by

ƒ 𝑥 = { 𝜆 𝑥2 − 2𝑥 𝑖𝑓 𝑥 ≤ 0

4𝑥 + 1 𝑖𝑓 𝑥 > 0

continuous at x = 0 ? What about continuity at x = 1.



42. Prove that f(x) = 𝑥 + 1 , is not differentiable at x = 1.

43. Discuss the continuity of ƒ 𝑥 = { 𝑠𝑖𝑛𝑥 − 𝑐𝑜𝑠𝑥 , 𝑥 ≠ 0 −1 , 𝑥 = 0 .

44. Differentiate: 𝑥𝑥 cos 𝑥 + 𝑥2+1

𝑥2−1

45. If x 1 + 𝑦 + y 1 + 𝑥 = 0 , proved that 𝑑𝑦

𝑑𝑥 = -

1

(𝑥+1)2 .

46. If x = a ( cos 𝑡 + t sin 𝑡 ) and y = a ( sin 𝑡 - t cos 𝑡 ), find 𝑑2𝑦/ 𝑑𝑥2.

47. If y = ( tan−1 𝑥)2 , show that ( 𝑥2 + 1 )2 𝑦2 + ( 𝑥2 + 1) 𝑦1 = 2 .

48. Differentiate: 𝑐𝑜𝑠 𝑥3 . 𝑠𝑖𝑛2𝑥2.

49. If y = sin−1 𝑥, then prove that ( 1- 𝑥2 )𝑑2𝑦

𝑑𝑥 2 - x 𝑑𝑦

𝑑𝑥 = 0

50. Differentiate: 𝑥2 + xy – sin 𝑥𝑦 = 0

Chapter 6- Application of Derivatives

51. Find the approximate value of 0.009 3

using derivative.

52. What will be the change in surface area of a cube if its edge is decreasing by 3%.

53. Find the equation of normals to the curve y = 𝑥3 + 2x + 6 which are parallel to the line

x + 14y + 4 = 0 .

54. The sum of the perimeter of a circle and a square is k, where k is some constant. Prove

that the sum of their areas is least when the side of square is double the radius of the

circle.

55. Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is

8/27 of the volume of the sphere.

56. Find the intervals in which ƒ(x) = 2 𝑥3 – 3 𝑥2 – 36 𝑥 + 7 is strictly increasing or

decreasing. Also find the maximum and minimum value of ƒ(x).

57. Find a point on the curve y = 𝑥 − 2 2 at which the tangents is parallel to the chord joining the point

( 2,0) and ( 4,4).

58. For the curve y = 4𝑥3 - 3 𝑥5, find the all points at which the tangents passes through the origin.

59. Prove that the curves x = 𝑦3 and xy = k cut at right angle if 8𝑘3 = 1.

60. Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of

height h and semi vertical angle 𝛼 is one third that of the cone and the greatest volume of cylinder is

4

27 𝜋 𝑕3 𝑡𝑎𝑛2𝛼

bhartiyam 12... · 3. what is triple fusion where and how it takes place. name the nuclei developed...

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